Question

Mr. Long puts $2,000 into a savings account for his daughters when they are born. He plans to give them the money in the account when it reaches $5,000. If the account earns 3.8% interest, compounded monthly, how old will his daughters be, to the nearest tenth of a year, when he gives them the money?

Answer 1

To find out how old Mr. Long's daughters will be when he gives them the money, we need to calculate when the savings account will reach $5,000 using the compound interest formula.

Step-by-step explanation:

To find out how old Mr. Long's daughters will be when he gives them the money, we need to calculate when the savings account will reach $5,000. We can use the formula for compound interest: A = P(1+r/n)^(nt), where A is the final amount, P is the initial principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, P = $2,000, A = $5,000, r = 3.8% = 0.038, and n = 12 (since interest is compounded monthly). We need to solve for t. Rearranging the formula, we get: t = (ln(A/P)) / (n * ln(1 + r/n)). After substituting the given values, we can calculate t to find out how old the daughters will be when they receive the money.

Using the above formula, the daughters will be approximately 25.8 years old when Mr. Long gives them the money.